Wenger deployed Walcott as Arsenal's lone hitman for the third game running and the move paid off handsomely as the 23-year-old bagged three well-taken goals and set up two more to lift the Gunners back up to fourth position in the Barclays Premier League.
Wenger said: "My desire is to extend his contract.
"I think he belongs here. Hopefully we can do it.
"I think he loves the club and the club loves him and the reciprocity in love is the most difficult to find.
"Today just typifies what I think he can do through the middle.
"The first goal was a Thierry Henry-type goal and he showed great determination with the third.
"He has become a good finisher. He has learned a lot because he is an intelligent player and because he is intelligent he will continue to improve."